Method and apparatus for linearizing a non-linear power amplifier

ABSTRACT

An apparatus and method for linearizing a non-linear power amplifier. The method comprises: performing an iteration algorithm by using a desired output signal of the non-linear power amplifier, to calculate an input signal of the non-linear power amplifier, whereby with the calculated input signal of the non-linear power amplifier, the non-linear power amplifier is linearized. The apparatus and method can produce a signal on the output of the non-linear power amplifier with an arbitrarily high quality of performance.

TECHNICAL FIELD

The present invention relates to a communication system, especially tothe linearization of a non-linear power amplifier in the communicationsystem.

BACKGROUND

A power amplifier (PA) is a device used in many communication systemswhich takes as input a low power desired signal and produces as output ahigher power version of the desired signal. Although PA's can be used aslinear devices, they are often pushed to operate in their non-linearregion because such operation can cause the PA to produce more outputpower and can also cause the PA to operate more efficiently. However,operating the PA in the nonlinear region comes at a cost in that theoutput of the PA now contains both a scaled up version of the desiredsignal, and also a significant amount of distortion.

Techniques exist whereby the signal coming into the PA is modified sothat although the input to the PA differs radically from the desiredsignal, the output coming out of the PA is, however, a scaled up versionof the desired signal. Some examples of techniques which can produce aPA input signal which will produce an arbitrary signal on the PA outputare digital predistortion (DPD) or analog predistortion based on acertain assumed PA model.

These techniques, however, are limited in performance because theyassume that the PA's characteristics can be modeled sufficiently by aspecific model. These assumed models are only accurate up to a certainlimit and hence the ultimate performance that can be obtained throughthe use of these techniques is also limited. It would be of benefit ifit would be possible to create an arbitrary output on any PA with anarbitrary amount of output signal quality performance.

Digital predistortion (DPD), as shown in FIG. 1 (prior art), refers to amethod in a communications system where the signal to be transmitted [5]is passed through a nonlinear predistortion function [2] before beingsent to the nonlinear power amplifier PA [1]. The general idea is thatthe nonlinear predistortion function [2] is chosen such that thecascaded combination of the nonlinear predistortion function [2] and thenonlinear PA [1] will produce a system that is linear overall. Thus, theactual PA output [6], will simply be a scaled up version of the input tothe predistortion function [2].

The predistortion function [2] is often inferred using the indirectlearning architecture as depicted in FIG. 1 (prior art). A coupler [4],is used to extract a small amount of the power generated by the PA [1].This signal is sent through an adaptable inverse PA model [3], whichproduces an output that is adapted to match, as closely as possible, theinput to the PA [1]. This adaptation is often implemented as an LMS oran RLS algorithm, although it is possible to use other algorithms.

Once the difference between the output of the of the inverse PA model[3] and the PA input is substantially small enough (as measured by thepower of the difference signal), the inverse PA model [3] is simplycopied and used directly as the predistortion function [2]. No modelinversion is necessary because the indirect learning architecturedescribed in FIG. 1 (prior art) directly calculates the inverse modelwithout first calculating the forward model.

Usually, this process needs to be repeated several times or over severaliterations before the output of the PA [1] is considered to besatisfactory, as measured by common signal transmission qualitymeasurements such as error vector magnitude (EVM) or adjacent channelleakage ration (ACLR).

A problem with the above structure is the difficulty in choosing themodel to be used for the inverse PA model [3]. Common structures thatare used are the Memory Polynomial (MP) or the Generalized MemoryPolynomial (GMP), although other models can also be used. Beforeactually trying a certain model, it is not clear which model will yieldthe best performance, and it is also not clear which specific parametersfor a particular model will yield the best performance. For example,with the Memory Polynomial model, one can specify both the maximum delayof the model and also the maximal nonlinear order of the model. It isnot clear, in advance, whether the GMP will perform better than the MPand which settings for maximum delay and nonlinear order in the MP willproduce the best results. Furthermore, because the PA [1] and theinverse PA model [3] are nonlinear entities, there are no known searchalgorithms available which will find the optimal models or modelsettings.

Typically, the inverse PA model is found by running the system in a labenvironment with a real PA. A certain model and certain model settingsare chosen and, after the system converges, one observes the finalsystem performance using measurements such as EVM and ACLR. Then, themodel and/or the settings are changed and the final system performanceis measured again. This procedure may proceed for hundreds ofmeasurements where each measurement may require several minutes of labtime. Finally, the model and settings which resulted in the bestperformance are chosen and used in the final system.

It would be beneficial if there was a method of improving the speed atwhich the optimal inverse PA model could be found.

An alternate form of DPD based on PA model inversion is shown in FIG. 2(prior art). As in the indirect learning architecture, the signal to betransmitted [5] is passed through a nonlinear predistortion function [2]before being sent to the nonlinear power amplifier PA [1]. The generalidea is that the nonlinear predistortion function [2] is chosen suchthat the cascaded combination of the nonlinear predistortion function[2] and the nonlinear PA [1] will produce a system that is linearoverall. Thus, the actual PA output [6], will simply be a scaled upversion of the input to the predistortion function [2].

With model inversion DPD, the forward PA model [7] is known and is anaccurate predictor of the PA's output, given a certain input. Thisforward PA model may arise from measurements of an actual PA, or it mayarise from a mathematical model derived by analyzing the circuit diagramof the PA. The key is that this model must be inverted and then used asthe predistortion function.

One of the major problems with this architecture is that although the PAforward model may in fact be very simple, the inversion of even a verysimple nonlinear model is often very difficult and requires a model thatis several orders more complex than the PA model itself.

It would be beneficial if a method existed to linearize the PA withoutneeding to invert the PA model.

DISCLOSURE OF INVENTION

An object of the present invention is to provide a method forlinearizing a non-linear power amplifier, which can produce a signal onthe output of the non-linear power amplifier with an arbitrarily highquality of performance. The method comprises: performing an iterationalgorithm by using a desired output signal of the non-linear poweramplifier, to calculate an input signal of the non-linear poweramplifier, whereby with the calculated input signal of the non-linearpower amplifier, the non-linear power amplifier is linearized.

In accordance with a certain embodiment of the invention, the iterationalgorithm is given by:

${{pa\_ in}_{n + 1} = {{pa\_ in}_{n} - {{alpha} \times \left( \frac{{pa\_ out}_{n} - {{pa\_ out}{\_ desired}}}{G_{n}} \right)}}},$

wherein pa_out_desired is the desired output signal of the non-linearpower amplifier, pa_in_(n) is the calculated input signal of thenon-linear power amplifier for iteration n, pa_out_(n) is a time alignedoutput signal of the non-linear power amplifier for iteration n, G_(n)is a gain of the non-linear power amplifier for iteration n which can becalculated by pa_in_(n) and pa_out_(n), and alpha is in a range from 0to 1, and wherein pa_in₁ is the desired output signal of the non-linearpower amplifier divided by an estimated gain of the non-linear poweramplifier.

In accordance with a further embodiment of the invention, the estimatedgain of the non-linear power amplifier is specified by a manufacturer ofthe non-linear power amplifier.

In accordance with a further embodiment of the invention, the estimatedgain of the non-linear power amplifier is obtained by measuring thenon-linear power amplifier when a low power signal is input into thenon-linear power amplifier.

In accordance with a further embodiment of the invention, the methodfurther comprises: performing a simulation algorithm by using thecalculated input signal of the non-linear power amplifier and acorresponding time aligned output signal of the non-linear poweramplifier, to simulate an inverse model of the non-linear poweramplifier, whereby the power amplifier is linearized by using thesimulated inverse model of the non-linear power amplifier.

In accordance with a further embodiment of the invention, the iterationalgorithm is given by:

${{{pa\_ mdl}{\_ in}{\_ corr}_{n,i}} = {{{pa\_ mdl}{\_ in}_{n,i}} - {{alpha} \times \left( \frac{{pa\_ out}_{n,i} - {{pa\_ out}{\_ desired}}}{G_{n,i}} \right)}}},$

wherein S_(n) represents segment n and is composed of samples n*B−M to(n+1)*B−1 of the desired output signal of the non-linear poweramplifier, pa_mdl_in_(n,i) is an input signal of a forward model of thenon-linear power amplifier for segment n and iteration i,pa_mdl_out_(n,i) is an output signal of the forward model of thenon-linear power amplifier for segment n and iteration i, G_(n,i) is angain of the forward model of the non-linear power amplifier for segmentn and iteration i which can be calculated by pa_mdl_in_(n,i) andpa_mdl_out_(n,i), alpha is in a range from 0 to 1, andpa_mdl_in_corr_(n,i) is an input correction signal for segment n anditeration i, wherein pa_mdl_in_(n,1) is S_(n) divided by an estimatedgain of the forward model, pa_mdl_in_(n,i+1) is obtained byconcatenating samples B to B+M−1 of pa_mdl_in_(n−1,end) and samples M toB+M−1 of pa_mdl_in_corr_(n,i), pa_mdl_in_(n−1,end) is an input signal ofa forward model of the non-linear power amplifier for segment n−1 of afinal iteration, and pa_mdl_in_(0,end) is 0, whereby the input signal ofthe non-linear power amplifier is obtained by concatenating samples M toB+M−1 of the input signals of the forward model of the non-linear poweramplifier of the last iteration for all segments, wherein the forwardmodel of the non-linear power amplifier is a zero delay and memorylimited forward model, and an output of the forward model is related toa current input sample and previous M−1 samples of the forward model.

Another object of the present invention is to provide an apparatus forlinearizing a non-linear power amplifier, which can produce a signal onthe output of the non-linear power amplifier with an arbitrarily highquality of performance. The apparatus comprises: a device for performingan iteration algorithm by using a desired output signal of thenon-linear power amplifier, to calculate an input signal of thenon-linear power amplifier, whereby with the calculated input signal ofthe non-linear power amplifier, the non-linear power amplifier islinearized.

In accordance with a certain embodiment of the invention, the iterationalgorithm is given by:

${{pa\_ in}_{n + 1} = {{pa\_ in}_{n} - {{alpha} \times \left( \frac{{pa\_ out}_{n} - {{pa\_ out}{\_ desired}}}{G_{n}} \right)}}},$

wherein pa_out_desired is the desired output signal of the non-linearpower amplifier, pa_in_(n) is the calculated input signal of thenon-linear power amplifier for iteration n, pa_out_(n) is a time alignedoutput signal of the non-linear power amplifier for iteration n, G_(n)is a gain of the non-linear power amplifier for iteration n which can becalculated by pa_in_(n) and pa_out_(n), and alpha is in a range from 0to 1; wherein pa_in₁ is the desired output signal of the non-linearpower amplifier divided by an estimated gain of the non-linear poweramplifier.

In accordance with a further embodiment of the invention, the estimatedgain of the non-linear power amplifier is specified by a manufacturer ofthe non-linear power amplifier.

In accordance with a further embodiment of the invention, the estimatedgain of the non-linear power amplifier is obtained by measuring thenon-linear power amplifier when a low power signal is input into thenon-linear power amplifier.

In accordance with a further embodiment of the invention, the apparatusfurther comprises: an electronic signal generator for repeatedlygenerating a signal which is the calculated input signal of thenon-linear power amplifier; a signal capturing device for capturing anoutput signal of the non-linear power amplifier, such that at least oneperiod of the signal being generated by the electronic signal generatoris captured; and a filter for filtering out frequencies that can not begenerated by the electronic signal generator and can not be captured bythe signal capturing device from a signal of subtracting pa_out_desiredfrom pa_out_(n).

In accordance with a further embodiment of the invention, bandwidths ofthe electronic signal generator and the signal capturing device arerelated to the non-linear power amplifier.

In accordance with a further embodiment of the invention, the signalcapturing device is configured to capture the output signal of thenon-linear power amplifier for iteration n more than one times, wherebyan averaged result of more than one captures is taken as pa_out_(n).

In accordance with a further embodiment of the invention, the apparatusfurther comprises: an inverse model of the signal capturing device forpost-processing the output signal of the non-linear power amplifiercaptured by the signal capturing device, whereby a linearity of thesignal capturing device can be improved.

In accordance with a further embodiment of the invention, the apparatusfurther comprises: a simulator for performing a simulation algorithm byusing the calculated input signal of the non-linear power amplifier anda corresponding time aligned output signal of the non-linear poweramplifier, to simulate an inverse model of the non-linear poweramplifier, whereby the power amplifier is linearized by using thesimulated inverse model of the non-linear power amplifier.

In accordance with a further embodiment of the invention, the iterationalgorithm is given by:

${{{pa\_ mdl}{\_ in}{\_ corr}_{n,i}} = {{{pa\_ mdl}{\_ in}_{n,i}} - {{alpha} \times \left( \frac{{pa\_ out}_{n,i} - {{pa\_ out}{\_ desired}}}{G_{n,i}} \right)}}},$

wherein S_(n) represents segment n and is composed of samples n*B−M to(n+1)*B−1 of the desired output signal of the non-linear poweramplifier, pa_mdl_in_(n,i) is an input signal of a forward model of thenon-linear power amplifier for segment n and iteration i,pa_mdl_out_(n,i) is an output signal of the forward model of thenon-linear power amplifier for segment n and iteration i, G_(n,i) is angain of the forward model of the non-linear power amplifier for segmentn and iteration i which can be calculated by pa_mdl_in_(n,i) andpa_mdl_out_(n,i), alpha is in a range from 0 to 1, andpa_mdl_in_corr_(n,i) is an input correction signal for segment n anditeration i, wherein pa_mdl_in_(n,1) is S_(n) divided by an estimatedgain of the forward model, pa_mdl_in_(n,i+1) is obtained byconcatenating samples B to B+M−1 of pa_mdl_in_(n−1,end) and samples M toB+M−1 of pa_mdl_in_corr_(n,i), pa_mdl_in_(n−1,end) is an input signal ofa forward model of the non-linear power amplifier for segment n−1 of afinal iteration, and pa_mdl_in_(0,end) is 0, whereby the input signal ofthe non-linear power amplifier is obtained by concatenating samples M toB+M−1 of the input signals of the forward model of the non-linear poweramplifier of the last iteration for all segments, wherein the forwardmodel of the non-linear power amplifier is a zero delay and memorylimited forward model, and an output of the forward model is related toa current input sample and previous M−1 samples of the forward model.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an indirect learning DPD;

FIG. 2 shows a PA model inversion DPD;

FIG. 3 shows a method of finding an ideal predistortion signal;

FIG. 4 shows an iterative DPD;

FIG. 5 shows system identification based on perfect captured data; and

FIG. 6 shows segmentation of pa_out_desired.

DETAILED DESCRIPTION OF THE INVENTION

One embodiment of the invention is implemented by placing the poweramplifier (PA) [1] in a measurement setup as shown in FIG. 3. The signalgoing to the power amplifier [1] comes from a device which can generatean arbitrary test signal which repeats cyclically, such as an electronicsignal generator (ESG) [11]. Because the PA is nonlinear, a large inputbandwidth is required to produce a certain clean output bandwidth. Thebandwidth of the ESG [11] typically must be 5-10 times the bandwidth ofthe desired operational bandwidth of the PA [1]. For example, if 5 MHzof clean signal are desired on the output, we may need to supply 25-50MHz of bandwidth on the input. But it should be noted that differentPA's will require a different amount of bandwidth from the ESG. Theoutput of the PA [1] is captured in a device capable of capturing atleast one full period of the signal being generated by the ESG [11],such as a programmable spectrum analyzer (PSA) [12]. The bandwidth ofthe PSA [12] must also be 5-10 times the bandwidth of the desiredoperational bandwidth of the PA [1]. The bandwidth of the PSA alsodepends on the particular PA.

In an actual lab environment, the ESG and the PSA may have differentsampling rates. However any of a number of well known techniques can beused to effectively change the sampling rate of the data captured by thePSA to be equal to the sampling rate of the data sent into the ESG.Therefore, the following text assumes that the captured signal, comingfrom the PSA, has been resampled to the sampling rate of the ESG.

The general concept is that the invention will iterate several times,and with each iteration, the output of the PA [1] will look more andmore like the desired PA output. In the first iteration, the signalgoing into the PA [1], pa_in₁ (with length N samples), from the ESG issimply the desired PA output signal scaled down by a rough estimate ofwhat the gain of the PA [1] will be (G_(e)). It is not necessary forG_(e) to be known very accurately and a rough estimate will do for thefirst iteration. For example the gain of the PA may be specified by themanufacturer and this value may be used as G_(e). Another possibility isthat a low power signal may be sent into the PA from the ESG and thepower of the signal coming out of the PA may be measured by the PSA. Inthis case, a rough estimate for G_(e) can be obtained as the square rootof the ratio of the power of the signal from the ESG and the power ofthe signal in the PSA.

$\begin{matrix}{{pa\_ in}_{1} = \frac{{pa\_ out}{\_ desired}}{G_{e}}} & {{Eq}\mspace{14mu} 1}\end{matrix}$

The repeating signal pa_in₁ is programmed into the ESG [11], and the PSA[12] then captures one complete period of the output of the PA [1].Because of delays inherent in the system, the captured signal will notbe perfectly time aligned with pa_in₁. Using cross-correlations, thecaptured signal can be shifted in time so that the delay between pa_in₁and the time shifted captured signal will be 0. After this timealignment, the time shifted captured signal for iteration n will becalled pa_out_(n). This time alignment is performed for each iteration.

Because a PA is only mildly nonlinear, the gain of the PA for this, orany subsequent iteration, can be estimated as:

$\begin{matrix}{G_{n} = \frac{\sum\limits_{i = 0}^{N - 1}{{pa\_ in}_{n}(i) \times {pa\_ out}_{n}(i)}}{\sum\limits_{i = 0}^{N - 1}{{pa\_ in}_{n}(i) \times {pa\_ in}_{n}(i)}}} & {{Eq}\mspace{14mu} 2}\end{matrix}$

Throughout this invention, complete sequences of signals will berepresented without an index. Specific samples of a signal will berepresented with an index. For example, pa_in_(n) represents the entirearray storing all the samples used by the ESG for iteration n.pa_in_(n)(i) represents the i'th element of the array of samplespa_in_(n). Because pa_in_(n) is of length N (as stated earlier), therange of value that i can take is 0 through N−1.

Again, because the PA is only mildly nonlinear, the output of the PA canbe considered to be composed of two components. One component is thedesired PA output, and the other component is a difference signal:

pa_out_(n)=pa_out_desired+diff′_(n)  Eq 3

diff_(n) =f _(B)(diff′_(n))=f _(B)(pa_out_(n)−pa_out_desired)  Eq 4

Where f_(B)(x) is the result of passing signal x through a zero-delayfilter whose effect is to remove any frequencies that cannot begenerated by the ESG and any frequencies that cannot be captured by thePSA. For example, this filter can be implemented by first taking an FFTof x, zeroing the frequencies that cannot be generated by the ESG,zeroing the frequencies that cannot be captured by the PSA, and finallyperforming an IFFT operation.

The idea is that during the next iteration, the input to the PA will beadjusted so as to cancel out the diff_(n) signal that was measuredduring the current iteration. Although the diff_(n) signal may becancelled out, new distortion products will be introduced which will becancelled out in future iterations of the algorithm. However, the newdistortion products will be at a lower power level and hence, as thealgorithm iterates the difference between the actual PA output and thedesired PA output will consistently decrease.

Specifically, the input for iteration n+1 is calculated as:

$\begin{matrix}{{pa\_ in}_{n + 1} = {{pa\_ in}_{n} - {{alpha} \times \frac{{diff}_{n}}{G_{n}}}}} & {{Eq}\mspace{14mu} 5}\end{matrix}$

Wherein, alpha takes on a value between 0.0 and 1.0. The closer alpha isto 1.0, the more quickly the algorithm will converge on a solution, butthe more unstable the algorithm may be. Typically, values of alphabetween 0.5 and 0.8 offer a good balance between convergence speed andstability. These values are determined experimentally and would varybetween different PA's.

The above procedure is demonstrated graphically in FIG. 4. The PA outputafter the first iteration is composed of the desired PA output [8], anda difference signal [9] indicated with a right-diagonally shaded box.The input used for the second iteration is composed of the originalinput to the PA and a signal designed to compensate for the differencesignal measured in the first iteration. This compensation component isindicated in the figure with a left-diagonally shaded box [10]. As canbe seen in the figure, on the output of the second iteration, theoriginal difference signal [9] is gone, but a new, smaller differencesignal has appeared. This new difference signal is removed with the nextiteration which in turn introduces a new, even smaller, differencesignal.

Although FIG. 4 only shows 4 iterations of this algorithm, thisiterative procedure can continue and the key issue is that theperformance of this algorithm is only limited by the noise performanceand nonlinearity of the PSA. For example, if the PSA introduces noiseinto the captured data, there is no way that a signal can be placedinside the ESG to compensate for the noise. Thus, we are limited inperformance by the noise and nonlinearities of the PSA. This means thatno matter which PA is inserted into the test setup, as long as the PA isonly mildly nonlinear (almost all PA's are only mildly nonlinear), thisprocedure will always be able to find a solution so that the PA outputwill be as similar as pa_out_desired up to the measurement limit of thePSA.

It should be noted that because the signals being used are repeatingcyclical signals, the noise performance of the PSA can be increased byforcing the PSA to perform several captures and then averaging theresults of the captures. For example, if two captures are performed andaveraged, this is equivalent to improving the noise performance of thePSA by 3 dB. Four captures would lead to a 6 dB improvement, and so on.This technique of performing multiple captures in the PSA can only beused to improve the noise performance of the PSA. If the PSA alsocontains nonlinearities, these nonlinearities cannot be reduced byperforming multiple captures.

Techniques do exist, however, which can be used to improve the linearityof the PSA. For example, separately, a known signal can be sent into thePSA and the output can be observed. A mathematical model can be builtwhich can model these nonlinearities and this model can be inverted.This inverse model can then be used to post-process the captured data soas to remove, or at least reduce, the nonlinearities in the PSA. Suchtechniques can be used to improve the linearity of the PSA and henceimprove the overall performance of the invention.

Iterations can be performed over and over until some performancerequirement has been met. For example, iterations can be performed untilthere is very little or no difference in the PA output between oneiteration and the next. Alternatively, iterations can be performed untilthe difference between the actual PA output and pa_out_desired becomessmaller than a certain threshold. Alternatively, a fixed number ofiterations can be performed.

The final predistorted signal going into the PA is called pa_in_(final)and the final signal coming out of the PA is pa_out_(final). Please notethat pa_out_(final) is basically the same as a scaled versionpa_out_desired with the only differences being those caused by themeasurement error of the PSA.

The major benefit of this method is that the PA can be made to producean arbitrary signal, with an arbitrary amount of signal fidelity,limited only by the measurement accuracy of the PSA. This is a majorimprovement over the prior art where the fidelity of the signal couldonly improve until a certain limit as determined by the accuracy of theunderlying PA model. Please note that PSA is only an example, and anydevice capable of capturing at least one full period of the signal beinggenerated by the ESG can be used to obtain this major benefit. Then, thesignal fidelity is only limited by the measurement accuracy of thisdevice.

In another embodiment of the invention, once the pa_in_(final) andpa_out_(final) signals are determined using the previous embodiment ofthe invention; they can be loaded up into a computer that can performsystem identification. Because the signals are stored in memory or inthe computer's hard drive, the computer can perform many rapidsimulations to determine which inverse PA model can best be used forpredistortion, and also which parameters should be applied to theinverse PA model so as to give the best performance. For performingthese rapid simulations, any system identification technique can beused.

This procedure can be contrasted with the one described in FIG. 1 (priorart), where each inverse PA model and each set of parameters for aparticular inverse PA model needed to be measured in a slow labenvironment. The procedure described above is several orders ofmagnitude faster than the prior art and, given the same amount of searchtime, allows for many more models to be searched so as to find the bestsolution.

Another embodiment of the invention arises when an accurate zero delay,memory limited model of the forward path of the PA is available. Such amodel is one for which the impulse response peaks at a time offset of 0,and for which the output is a function of only the current input sampleand the previous M−1 samples, for finite M. Note that for some nonlinearmodels, it may be difficult or impossible to calculate a meaningfulimpulse response. For such models, it suffices that for typical signalsto be transmitted through the PA, the cross-correlation between the PAmodel's input and the PA model's output peaks at a time offset of 0.This model may come from measurements of a PA, or perhaps it can bederived from a mathematical analysis of the PA's circuit diagram. It isnoted that the performance of this embodiment is limited by the accuracyof the PA model.

The first step is that the desired PA output signal, pa_out_desired(n),must be broken up into smaller segments. The length of each segment isB+M. B is the number of PA output samples that will be produced fromeach segment and depends on the implementation. The larger B is, themore efficient the algorithm, but also the larger the delay in creatingthe PA's input signal. This is a design parameter that will bedetermined by the particular implementation that has been chosen torealize this invention.

Segment n (S_(n)) of length B+M is composed of samples n*B−M through(n+1)*B−1 of pa_out_desired as indicated by the following notation:

S _(n)=pa_out_desired(n*B−M:(n+1)*B−1)  Eq 6

FIG. 6 is a graphical depiction of how pa_out_desired can be split upinto several segments. The brackets indicate the segments of length B+Msamples. Please note that the signal can be segmented in any manner aslong as each segment is of length B+M and the overlap between segmentsis M. This is just one manner in which pa_out_desired can be segmented.

Each segment is processed individually using the following iterativeprocedure.

First, the signal going into the PA model (pa_mdl_in) for segment n,iteration 1 is created as follows:

$\begin{matrix}{{{pa\_ mdl}{\_ in}_{n,1}} = \frac{S_{n}}{G_{e}}} & {{Eq}\mspace{14mu} 7}\end{matrix}$

G_(e) is a rough estimate of the gain of the PA model and is only usedfor the first iteration. It is not necessary for this number to be veryaccurate and a rough estimate is good enough. One method that can beused to estimate G_(e) is that first, a random noise signal with anaverage power level similar to the typical power level expected to beinput to the PA model can be generated. The PA model can be simulatedand the average power of the signal on the output of the PA model can bemeasured. G_(e) can simply be set to be the square root of the ratio ofthe power of the output signal divided by the power of the input signal.

pa_mdl_in_(n,1) is sent through the PA model to produce pa_mdl_out_(n,1)which also is of length B+M. The gain for this iteration or any otheriteration i can be calculated as:

$\begin{matrix}{G_{n,i} = \frac{\sum\limits_{k = 0}^{B + M - 1}{{pa\_ mdl}{\_ in}_{n,i}(k) \times {pa\_ mdl}{\_ out}_{n,i}(k)}}{\sum\limits_{k = 0}^{B + M - 1}{{pa\_ mdl}{\_ in}_{n,i}(k) \times {pa\_ mdl}{\_ in}_{n,i}(k)}}} & {{Eq}\mspace{14mu} 8}\end{matrix}$

Then, a difference signal for segment n, iteration i is calculated as:

diff_(n,i)=pa_mdl_out_(n,i) −S _(n)  Eq 9

A correction signal is calculated as:

$\begin{matrix}{{{pa\_ mdl}{\_ in}{\_ corr}_{n,i}} = {{{pa\_ mdl}{\_ in}_{n,i}} - {{alpha} \times \frac{{diff}_{n,i}}{G_{n,i}}}}} & {{Eq}\mspace{14mu} 10}\end{matrix}$

Where alpha is a constant that takes a value between 0 and 1. The closeralpha is to 1, the faster the convergence, but the higher the risk ofinstability. Typically, alpha will have a value between 0.5 and 0.8.

Finally, to complete this iteration, the PA model input signal for thenext iteration is created:

pa_mdl_in_(n,i+1)={pa_mdl_in_(n−1,end)(B:B+M−1),pa_mdl_in_corr_(n,i)(M:B+M−1)}  Eq11

Where the notation {A,B} indicates that the two sequences A and B shouldbe concatenated together. Furthermore, pa_mdl_in_(n,end) indicates thevalue of pa_mdl_in after the final iteration of processing for segmentn.

It should be noted that pa_mdl_in_(n,i+1) depends onpa_mdl_in_(n−1,end). If pa_mdl_in_(n−1,end) is not available, thissignal can be replaced by zeros in the above equation.pa_mdl_in_(n−1,end) is not available, for instance, when the first Ssegment is being processed.

This iterative process can continue and with each iteration i,pa_mdl_out_(n,i) will start to look more and more like S_(n). Theiteration process can continue for a fixed number of iterations, or anautomatic iteration termination mechanism can be used. For example, onepossibility is to keep iterating until the error power of the differencebetween pa_mdl_out_(n,i) and S_(n) becomes lower than a certainthreshold.

The signal applied to the PA is created as:

Eq 12 pa_in = { pa_mdl_in_(0,end)(M : B + M − 1), pa_mdl_in_(1,end)(M :B + M − 1), pa_mdl_in_(2,end)(M : B + M − 1), ... }

In an typical realization using, for example, an FPGA, simultaneouslywhile pa_mdl_in_(n,end)(M:B+M−1) is being sent to the PA,pa_mdl_in_(n+1,end) will be calculated using the iterative processdescribed above.

The primary advantage of this embodiment of the invention is thatwhereas the prior art shown in FIG. 2 attempted to mathematically inverta model, this embodiment of the invention does not need to perform modelinversion at all. It can generate the correct PA input given only aforward model of the PA. Because this embodiment of the invention doesnot attempt to invert a nonlinear model, no model inversion errors areintroduced.

While several embodiments of the invention have been illustrated anddescribed, it is not intended that these embodiments illustrate anddescribe all possible forms of the invention. Rather, the words used inthe specification are words of description rather than limitation, andit is understood that various changes and modifications may be madewithout departing from the spirit and scope of the invention.

1. A method for linearizing a non-linear power amplifier, comprising:performing an iteration algorithm by using a desired output signal ofthe non-linear power amplifier, to calculate an input signal of thenon-linear power amplifier, whereby with the calculated input signal ofthe non-linear power amplifier, the non-linear power amplifier islinearized.
 2. A method according to claim 1, wherein the iterationalgorithm is given by:${{pa\_ in}_{n + 1} = {{pa\_ in}_{n} - {{alpha} \times \left( \frac{{pa\_ out}_{n} - {{pa\_ out}{\_ desired}}}{G_{n}} \right)}}},$wherein pa_out_desired is the desired output signal of the non-linearpower amplifier, pa_in_(n) is the calculated input signal of thenon-linear power amplifier for iteration n, pa_out_(n) is a time alignedoutput signal of the non-linear power amplifier for iteration n, G_(n)is a gain of the non-linear power amplifier for iteration n which can becalculated by pa_in_(n) and pa_out_(n), and alpha is in a range from 0to 1, and wherein pa_in₁ is the desired output signal of the non-linearpower amplifier divided by an estimated gain of the non-linear poweramplifier.
 3. A method according to claim 2, wherein the estimated gainof the non-linear power amplifier is specified by a manufacturer of thenon-linear power amplifier.
 4. A method according to claim 2, whereinthe estimated gain of the non-linear power amplifier is obtained bymeasuring the non-linear power amplifier when a low power signal isinput into the non-linear power amplifier.
 5. A method according toclaim 1, further comprising: performing a simulation algorithm by usingthe calculated input signal of the non-linear power amplifier and acorresponding time aligned output signal of the non-linear poweramplifier, to simulate an inverse model of the non-linear poweramplifier, whereby the power amplifier is linearized by using thesimulated inverse model of the non-linear power amplifier.
 6. A methodaccording to claim 1, wherein the iteration algorithm is given by:${{{pa\_ mdl}{\_ in}{\_ corr}_{n,i}} = {{{pa\_ mdl}{\_ in}_{n,i}} - {{alpha} \times \left( \frac{{{pa\_ mdl}{\_ out}_{n,i}} - S_{n}}{G_{n,i}} \right)}}},$wherein S_(n) represents segment n and is composed of samples n*B−M to(n+1)*B−1 of the desired output signal of the non-linear poweramplifier, pa_mdl_in_(n,i) is an input signal of a forward model of thenon-linear power amplifier for segment n and iteration i,pa_mdl_out_(n,i) is an output signal of the forward model of thenon-linear power amplifier for segment n and iteration i, G_(n,i) is angain of the forward model of the non-linear power amplifier for segmentn and iteration i which can be calculated by pa_mdl_in_(n,i) andpa_mdl_out_(n,i), alpha is in a range from 0 to 1, andpa_mdl_in_corr_(n,i) is an input correction signal for segment n anditeration i, wherein pa_mdl_in_(n,1) is S_(n) divided by an estimatedgain of the forward model, pa_mdl_in_(n,i+1) is obtained byconcatenating samples B to B+M−1 of pa_mdl_in_(n−1,end) and samples M toB+M−1 of pa_mdl_in_corr_(n,i), pa_mdl_in_(n−1,end) is an input signal ofa forward model of the non-linear power amplifier for segment n−1 of afinal iteration, and pa_mdl_in_(0,end) is 0, whereby the input signal ofthe non-linear power amplifier is obtained by concatenating samples M toB+M−1 of the input signals of the forward model of the non-linear poweramplifier of the last iteration for all segments, wherein the forwardmodel of the non-linear power amplifier is a zero delay and memorylimited forward model, and an output of the forward model is related toa current input sample and previous M−1 samples of the forward model. 7.An apparatus for linearizing a non-linear power amplifier, comprising: adevice for performing an iteration algorithm by using a desired outputsignal of the non-linear power amplifier, to calculate an input signalof the non-linear power amplifier, whereby with the calculated inputsignal of the non-linear power amplifier, the non-linear power amplifieris linearized.
 8. An apparatus according to claim 7, wherein theiteration algorithm is given by:${{pa\_ in}_{n + 1} = {{pa\_ in}_{n} - {{alpha} \times \left( \frac{{pa\_ out}_{n} - {{pa\_ out}{\_ desired}}}{G_{n}} \right)}}},$wherein pa_out_desired is the desired output signal of the non-linearpower amplifier, pa_in_(n) is the calculated input signal of thenon-linear power amplifier for iteration n, pa_out_(n) is a time alignedoutput signal of the non-linear power amplifier for iteration n, G_(n)is a gain of the non-linear power amplifier for iteration n which can becalculated by pa_in_(n) and pa_out_(n), and alpha is in a range from 0to 1; wherein pa_in₁ is the desired output signal of the non-linearpower amplifier divided by an estimated gain of the non-linear poweramplifier.
 9. An apparatus according to claim 8, wherein the estimatedgain of the non-linear power amplifier is specified by a manufacturer ofthe non-linear power amplifier.
 10. An apparatus according to claim 8,wherein the estimated gain of the non-linear power amplifier is obtainedby measuring the non-linear power amplifier when a low power signal isinput into the non-linear power amplifier.
 11. An apparatus according toclaim 8, further comprising: an electronic signal generator forrepeatedly generating a signal which is the calculated input signal ofthe non-linear power amplifier; a signal capturing device for capturingan output signal of the non-linear power amplifier, such that at leastone period of the signal being generated by the electronic signalgenerator is captured; and a filter for filtering out frequencies thatcan not be generated by the electronic signal generator and can not becaptured by the signal capturing device from a signal of subtractingpa_out_desired from pa_out_(n).
 12. An apparatus according to claim 11,bandwidths of the electronic signal generator and the signal capturingdevice are related to the non-linear power amplifier.
 13. An apparatusaccording to claim 11, the signal capturing device is configured tocapture the output signal of the non-linear power amplifier foriteration n more than one times, whereby an averaged result of more thanone captures is taken as pa_out_(n).
 14. An apparatus according to claim11, further comprising: an inverse model of the signal capturing devicefor post-processing the output signal of the non-linear power amplifiercaptured by the signal capturing device, whereby a linearity of thesignal capturing device can be improved.
 15. An apparatus according toclaim 7, further comprising: a simulator for performing a simulationalgorithm by using the calculated input signal of the non-linear poweramplifier and a corresponding time aligned output signal of thenon-linear power amplifier, to simulate an inverse model of thenon-linear power amplifier, whereby the power amplifier is linearized byusing the simulated inverse model of the non-linear power amplifier. 16.An apparatus according to claim 7, wherein the iteration algorithm isgiven by:${{{pa\_ mdl}{\_ in}{\_ corr}_{n,i}} = {{{pa\_ mdl}{\_ in}_{n,i}} - {{alpha} \times \left( \frac{{{pa\_ mdl}{\_ out}_{n,i}} - S_{n}}{G_{n,i}} \right)}}},$wherein S_(n) represents segment n and is composed of samples n*B−M to(n+1)*B−1 of the desired output signal of the non-linear poweramplifier, pa_mdl_in_(n,i) is an input signal of a forward model of thenon-linear power amplifier for segment n and iteration i,pa_mdl_out_(n,i) is an output signal of the forward model of thenon-linear power amplifier for segment n and iteration i, G_(n,i) is angain of the forward model of the non-linear power amplifier for segmentn and iteration i which can be calculated by pa_mdl_in_(n,i) andpa_mdl_out_(n,i), alpha is in a range from 0 to 1, andpa_mdl_in_corr_(n,i) is an input correction signal for segment n anditeration i, wherein pa_mdl_in_(n,1) is S_(n) divided by an estimatedgain of the forward model, pa_mdl_in_(n,i+1) is obtained byconcatenating samples B to B+M−1 of pa_mdl_in_(n−1,end) and samples M toB+M−1 of pa_mdl_in_corr_(n,i), pa_mdl_in_(n−1,end) is an input signal ofa forward model of the non-linear power amplifier for segment n−1 of afinal iteration, and pa_mdl_in_(0,end) is 0, whereby the input signal ofthe non-linear power amplifier is obtained by concatenating samples M toB+M−1 of the input signals of the forward model of the non-linear poweramplifier of the last iteration for all segments, wherein the forwardmodel of the non-linear power amplifier is a zero delay and memorylimited forward model, and an output of the forward model is related toa current input sample and previous M−1 samples of the forward model.